$SL(2, Z)$ invariant rotating $(m,n)$ strings in $AdS_3\times S^3$ with mixed flux

TL;DR

This paper investigates the dynamics of $(m,n)$ strings in an $AdS_3 imes S^3$ background with mixed flux, revealing new solutions like giant magnons and spikes, and analyzing their conserved charges.

Contribution

It introduces $SL(2,Z)$-covariant analysis of rotating and pulsating $(m,n)$ strings in mixed flux backgrounds, deriving novel solutions and charge relations.

Findings

Derived dyonic giant magnon solutions.

Found single spike solutions with conserved charge relationships.

Analyzed pulsating $(m,n)$ strings in $AdS_3$ with mixed flux.

Abstract

We study rigidly rotating and pulsating $(m,n)$ strings in $AdS_3 \times S^3$ with mixed three form flux. The $AdS_3 \times S^3$ background with mixed three form flux is obtained in the near horizon limit of $SL(2,Z)$-transformed solution, corresponding to the bound state of NS5-branes and fundamental strings. We study the probe $(m,n)-$string in this background by solving the manifest $SL(2,Z)-$covariant form of the action. We find out the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find out various relationships among the conserved charges. We further study a class of pulsating $(m,n)$ string in $AdS_3$ with mixed three form flux.